Golf club face thickness optimization method

ABSTRACT

A method of optimizing golf club head and golf ball design is disclosed herein. The method includes inputting a RBF for stress, a RBF for CT and a RBF for ball speed into an Adaptive Simulated Annealing algorithm to generate an optimized structure for the club head for ball speed.

CROSS REFERENCES TO RELATED APPLICATIONS

The Present Application is a continuation-in-part application of U.S.patent application Ser. No. 16/424,758, filed on May 29, 2019, whichclaims priority to U.S. Provisional Patent Application No. 62/677,805,filed on May 30, 2018, each of which is hereby incorporated by referencein its entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not Applicable

BACKGROUND OF THE INVENTION Field of the Invention

The present invention relates to a golf club head and golf ball designoptimization method. More specifically, the present invention isdirected to a face thickness optimization method that yields novel,high-performance, variable face thickness patterns for golf club heads.

Description of the Related Art

The prior art discloses numerous golf club heads with variable facethickness patterns. Some examples include 6354962, 6368234, 6435977,6398666, 6623377, 6491592, 6582323, 7137907, 7101289, 7258626, 8012041,and 8696489. However, the prior art fails to disclose a method ofoptimizing, for a given golf club head, the variable face thicknesspattern, and efficiently manufacturing a face having that pattern.

BRIEF SUMMARY OF THE INVENTION

The method of the present invention is a computer-aid optimizationanalysis yielding variable face thickness patterns for golf club headsthat achieve large increases in coefficient of restitution (COR) whileconforming to USGA and R&A regulations.

One aspect of the present invention is a non-transitory computerreadable medium storing instructions that optimize the structure of agolf club head for ball speed, when executed by a processor of anapparatus.

Another aspect of the present invention is a method for optimizing thestructure of a golf club head for ball speed.

Yet another aspect of the present invention is a method for optimizingthe structure of a golf club head for ball speed. The method includesgenerating a radial basis function (“RBF”) for stress of a golf clubhead from a finite element analysis (“FEA”) program using a plurality offace thickness points for the golf club head and a plurality of bodythickness points for the golf club head. The method also includesgenerating a RBF for characteristic time (“CT”) of a golf club head froma FEA program using a plurality of face thickness points for the golfclub head and a plurality of body thickness points for the golf clubhead. The method also includes generating a RBF for ball speed of a golfclub head from a FEA program using a plurality of face thickness pointsfor the golf club head and a plurality of body thickness points for thegolf club head. The method also includes inputting the RBF for stress,the RBF for CT and the RBF for ball speed into an Adaptive SimulatedAnnealing algorithm to generate an optimized structure for the club headfor ball speed.

Yet another aspect of the present invention is a non-transitory computerreadable medium storing instructions that optimize the structure of agolf club head for ball speed, when executed by a processor of anapparatus, cause the apparatus to: generate a radial basis function(“RBF”) for stress of a golf club head from a finite element analysis(“FEA”) program using a plurality of face thickness points for the golfclub head and a plurality of body thickness points for the golf clubhead; generate a RBF for characteristic time (“CT”) of a golf club headfrom a FEA program using a plurality of face thickness points for thegolf club head and a plurality of body thickness points for the golfclub head; generate a RBF for ball speed of a golf club head from a FEAprogram using a plurality of face thickness points for the golf clubhead and a plurality of body thickness points for the golf club head;and input the RBF for stress, the RBF for CT and the RBF for ball speedinto an Adaptive Simulated Annealing algorithm to generate an optimizedstructure for the club head for ball speed.

Yet another aspect of the present invention is an apparatus comprising aprocessor and a memory. The memory stores computer readable instructionsthat, when executed by the processor, cause the apparatus to: generate aradial basis function (“RBF”) for stress of a golf club head from afinite element analysis (“FEA”) program using a plurality of facethickness points for the golf club head and a plurality of bodythickness points for the golf club head; generate a RBF forcharacteristic time (“CT”) of a golf club head from a FEA program usinga plurality of face thickness points for the golf club head and aplurality of body thickness points for the golf club head; generate aRBF for ball speed of a golf club head from a FEA program using aplurality of face thickness points for the golf club head and aplurality of body thickness points for the golf club head; and input theRBF for stress, the RBF for CT and the RBF for ball speed into anAdaptive Simulated Annealing algorithm to generate an optimizedstructure for the club head for ball speed.

Yet another aspect of the present invention is a method for optimizingthe structure of a golf club head for ball speed. The method includesgenerating a radial basis function (“RBF”) for stress of a golf clubhead from a finite element analysis (“FEA”) program using a plurality offace thickness points for the golf club head and a plurality of bodythickness points for the golf club head. The method also includesgenerating a RBF for characteristic time (“CT”) of a golf club head froma FEA program using a plurality of face thickness points for the golfclub head and a plurality of body thickness points for the golf clubhead. The method also includes generating a RBF for ball speed of a golfclub head from a FEA program using a plurality of face thickness pointsfor the golf club head and a plurality of body thickness points for thegolf club head. The method also includes inputting a constrained RBF forstress, a constrained RBF for CT and the RBF for ball speed into ameta-modeled based optimization algorithm to generate an optimizedstructure for the club head for ball speed.

Yet another aspect of the present invention is a non-transitory computerreadable medium storing instructions that optimize the structure of agolf club head for ball speed, when executed by a processor of anapparatus, cause the apparatus to: generate a radial basis function(“RBF”) for stress of a golf club head from a finite element analysis(“FEA”) program using a plurality of face thickness points for the golfclub head and a plurality of body thickness points for the golf clubhead; generate a RBF for characteristic time (“CT”) of a golf club headfrom a FEA program using a plurality of face thickness points for thegolf club head and a plurality of body thickness points for the golfclub head; generate a RBF for ball speed of a golf club head from a FEAprogram using a plurality of face thickness points for the golf clubhead and a plurality of body thickness points for the golf club head;and input a constrained RBF for stress, a constrained RBF for CT and theRBF for ball speed into a meta-modeled based optimization algorithm togenerate an optimized structure for the club head for ball speed.

Yet another aspect of the present invention is an apparatus comprising aprocessor and memory. The memory stores computer readable instructionsthat, when executed by the processor, cause the apparatus to: generate aradial basis function (“RBF”) for stress of a golf club head from afinite element analysis (“FEA”) program using a plurality of facethickness points for the golf club head and a plurality of bodythickness points for the golf club head; generate a RBF forcharacteristic time (“CT”) of a golf club head from a FEA program usinga plurality of face thickness points for the golf club head and aplurality of body thickness points for the golf club head; generate aRBF for ball speed of a golf club head from a FEA program using aplurality of face thickness points for the golf club head and aplurality of body thickness points for the golf club head; and input aconstrained RBF for stress, a constrained RBF for CT and the RBF forball speed into a meta-modeled based optimization algorithm to generatean optimized structure for the club head for ball speed.

Yet another aspect of the present invention is a non-transitory computerreadable medium storing instructions that optimize the structure of aputter head for ball speed robustness. The computer readable medium,when executed by a processor, causes the processor to generate aplurality of face thickness points and a plurality of body thicknesspoints using a sampling technique to fill a design space using a finiteelement analysis (“FEA”) program to generate a plurality of responsescomprising a plurality of performance characteristics for the putterhead. The computer readable medium also causes the processor to generatea surrogate model from the plurality of responses comprising generatinga function for durability of the putter head from a finite elementanalysis (“FEA”) program of the putter head using the plurality of facethickness points for the golf club head and the plurality of bodythickness points for the putter head, and generating a function for ballspeed robustness of the putter head from the FEA program using theplurality of face thickness points for the putter head and the pluralityof body thickness points for the putter head. The computer readablemedium also causes the processor to use the surrogate model in anoptimization algorithm to provide an approximation of a lower samplespace. The computer readable medium also causes the processor to repeata process until the surrogate model converges with the FEA for apredetermined objective to optimize the structure of a golf club headfor ball speed robustness.

Yet another aspect of the present invention is an apparatus comprising aprocessor and memory storing computer readable instructions. Thecomputer readable instructions when executed by the processor, cause theapparatus to generate a function for stress of a putter head from afinite element analysis (“FEA”) program using a plurality of facethickness points for the golf club head and a plurality of bodythickness points for the golf club head. The computer readableinstructions also cause the apparatus to generate a function for ballspeed robustness of the putter head from the FEA program using theplurality of face thickness points for the putter head and the pluralityof body thickness points for the putter head. The computer readableinstructions also cause the apparatus to input a constrained functionfor stress and the function for ball speed robustness into ameta-modeled based optimization algorithm to generate an optimizedstructure for the putter head for ball speed robustness.

Yet another aspect of the present invention is an apparatus comprising aprocessor and memory storing computer readable instructions. Thecomputer readable instructions when executed by the processor, cause theapparatus to generate a function for the durability of an iron-type clubhead from a finite element analysis (“FEA”) program using a plurality offace thickness points for the golf club head and a plurality of bodythickness points for the iron-type club head. The computer readableinstructions also cause the apparatus to generate a function for ballspeed of the iron-type club head from the FEA program using theplurality of face thickness points for the iron-type club head and theplurality of body thickness points for the iron-type club head. Thecomputer readable instructions also cause the apparatus to input aconstrained function for stress and the function for ball speed into ameta-modeled based optimization algorithm to generate an optimizedstructure for the iron-type club head for ball speed.

Yet another aspect of the present invention is a non-transitory computerreadable medium storing instructions that structure of an iron-type clubhead for ball speed. The computer readable medium, when executed by aprocessor, causes the processor to generate a plurality of facethickness points and a plurality of body thickness points using asampling technique to fill a design space using a finite elementanalysis (“FEA”) program to generate a plurality of responses comprisinga plurality of performance characteristics for the iron-type club head.The computer readable medium also causes the processor to generate asurrogate model from the plurality of responses comprising generating afunction for durability of the iron-type club head from a finite elementanalysis (“FEA”) program of the iron-type club head using the pluralityof face thickness points for the golf club head and the plurality ofbody thickness points for the putter head, and generating a function forball speed of the iron-type club head from the FEA program using theplurality of face thickness points for the iron-type club head and theplurality of body thickness points for the iron-type club head. Thecomputer readable medium also causes the processor to use the surrogatemodel in an optimization algorithm to provide an approximation of alower sample space. The computer readable medium also causes theprocessor to repeat a process until the surrogate model converges withthe FEA for a predetermined objective to optimize the structure of theiron-type club head for ball speed. Use the surrogate model in anoptimization algorithm to provide an approximation of a lower samplespace comprises inputting a constrained function for durability and thefunction for ball speed into a meta-modeled based optimization algorithmto generate an optimized structure for the iron-type club head for ballspeed.

Having briefly described the present invention, the above and furtherobjects, features, and advantages thereof will be recognized by thoseskilled in the pertinent art from the following detailed description ofthe invention when taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

FIG. 1 is a flow chart illustrating a method of the present invention.

FIG. 2 is a face insert with a variable thickness pattern derived fromthe method shown in FIG. 1 .

FIG. 3 is a thickness map of the face insert shown in FIG. 2 .

FIG. 4 is a putter face insert with a variable thickness pattern derivedfrom the method shown in FIG. 1 .

FIG. 5 is a putter face insert with a variable thickness pattern derivedfrom the method shown in FIG. 1 .

FIG. 6 is an iron-type face insert with a variable thickness patternderived from the method shown in FIG. 1 .

DETAILED DESCRIPTION OF THE INVENTION

The present invention preferably uses an explicit based Finite ElementAnalysis (FEA) method in LS-Dyna® software to run impacts of a simulatedgolf ball into a simulated driver. LS-Dyna® results are preferablyderived for full launch performance metrics, and manage durability,conformance, and sound. While existing techniques to run LS-Dyna® haveimproved, each iteration of the design output previously was guided bythe stress of the solution. Simple two- or three-parameter experimentaldesigns examined the correlation coefficients between variables and ballspeed and CT, which required a great deal of analyst skill and time.

The method of the present invention increases the usefulness of FEA byusing more of its data and making design exploration lessanalyst-dependent, thereby achieving optimized results within a designspace. It also provides a solution that considers any number of designparameters and is easier to use.

A method 100 for optimizing the structure of a golf club head for ballspeed is shown in FIG. 1 . At block 101, a sampling method is used tocreate a range of design parameters to create multiple designs forfinite element analysis. At block 102, a finite element analysis is runto supply results needed to create a neural net model of a design. Atblock 103, a neural net model is used in an optimization routine topredict an optimal point for the design based on an objective. At block104, the optimal design is run through finite element analysis andcomparing it against the prediction. At block 105, the steps arerepeated with a new sampling until a converged design is achieved,wherein the converged design is selected from the group consisting of agolf club head component and a golf ball. This method differs fromguided machine learning routines in that the training set comprisesdesigns from the sampling method and the hold out is the optimal result.This process is continued until an accurate model is provided or theresults do not change from significantly from prior iterations.

The method of the present invention was utilized to design the variablethickness face design 200 shown in FIG. 2 and the face design 300 shownin FIG. 3 . In this instance, the solution comprised selectingpreferably from ten to hundred design parameters, more preferably fromtwenty to seventy design parameters, and most preferably thirty-fourdesign parameters and running over one thousand design variations onthese design parameters to achieve an optimized solution based on thefollowing series of constraints: (1) a 200 Ksi stress constraint basedon a Titanium 6-4 sheet material, (2) a 248 μs characteristic time (CT)constraint (for conformance purposes), and (3) a 196 gram head mass. Theresulting design maximizes the coefficient of restitution of the face.The sampling was performed with a space filling algorithm, modeled witha Radial basis function, and optimized with a hybrid Adaptive SimulatedAnnealing algorithm to find the global optimal. LFOP was used to findthe optimal result in the identified global optimal region.

Once the variable thickness pattern shown in FIGS. 2 and 3 wasdetermined using the method of the present invention, forging andmachining processes were used to manufacture the optimized face insert.

A variable thickness face insert designed using the method of thepresent invention may be incorporated into a standard golf club head, ormay be combined with a body having other structural, mass-propertiesenhancing features. For example, the insert can be placed into a bodywith face stress-reducing features, such as those disclosed in U.S. Pat.Nos. 9,486,677, 9,597,558, 9,597,561, 9,687,701, 9,687,702, 9,694,257,9,757,629, 9,776,058, 9,814,947, 9,821,199, 9,855,476, and 9,889,349,the disclosure of each of which is hereby incorporated by reference inits entirety herein. The insert may, alternatively, be combined with abody comprising one or more slots, channels, or grooves, such as thosedisclosed in U.S. Pat. Nos. 8,403,771, 8,529,368, 8,858,360, 8,956,242,9,468,819, and 9,776,057, the disclosure of each of which is herebyincorporated by reference in its entirety herein. The insert may also becombined with a body having one or more stationary or movable weightmembers, such as those disclosed in U.S. Pat. Nos. 8,257,195, 8,328,661,8,414,420, 8,425,346, 8,900,070, 8,926,448, 9,211,451, 9,586,105,9,782,642, 8,894,506, 9,084,921, 8,696,491, 9,387,376, 9,675,856,9,211,453, 9,289,660, 9,364,728, 8,790,195, 8,968,116, 9,623,294,9,694,261, 9,636,553, 9,682,296, 9,694,256, 8,690,708, 9,022,881,9,101,811, 8,834,294, 8,956,244, 9,067,110, 9,072,951, 9,180,349,9,216,332, and 9,308,423, the disclosure of each of which is herebyincorporated by reference in its entirety herein.

When designing a golf ball using this method, accurate material modelsare required to achieve the level of detail needed for the results. Thisadvanced accuracy requires a combination of lab-generated data fromcyclic compression tests, drop tests, and Split-Hopkinson bar tests onthe material, in addition to matching simulation results to PTM COR dataon ball cores. This data is used to tune the material models by nineparameters. It uses the same techniques that are used to design theface. The only difference is that, instead of being constrained bystress, CT, and mass, the simulation objective is to minimize thedifference between the test results and simulation data. The model fitswhere verified, using data from multilayer core tests. The result of0.0008 COR point delta on the dual core is within two times themeasurement error of the test, so combining material in the simulationcan be as accurate as the physical test results. Results are provided inTable 1 below.

TABLE 1 Tested FEA COR Material Diameter COR COR Delta −10 Comp 0.9380.760001 0.759925  7.6E−05 −10 Comp 1.615 0.76947  0.769612 −1.40E−04 90Comp 0.938 0.768   0.767927  7.26E−05 90 Comp 1.615 0.783   0.782968 3.17E−05 Dual Core 90 comp 1.542 0.784   0.783196  8.04E−04 outer − 10comp inner

The method of the present invention optimizes golf balls and clubs foruse with each other, while keeping these products in conformance withtheir respective rules. Simultaneous design gives a larger design spacefor exploration.

In alternative embodiments shown in FIGS. 4 and 5 , the thicknesses ofputter face inserts 400, 500 are optimized to minimize ball speedvariation across the face on a nine point hit map, while keeping overallputter head mass between 340 and 360 grams, and more preferably between347 and 351 grams. The face inserts 400, 500 each have at least foursides 402, 404, 406, 408, 502, 504, 506, 508, and may be composed of anymetal alloy material, but preferably are selected from the groupconsisting of Aluminum 6061, Titanium 6-4, and 304 SS. They may beformed, forged, metal injection molded, printed by a three-dimensionalprinter, cast, and/or milled.

As shown in Table 2 below, the ball speed robustness of the optimizedface insert 400 shown in FIG. 4 is improved when compared with existingToulon San Diego and Microhinge Star putters, both sold by Callaway GolfCompany.

TABLE 2 Improvement Improvement Head Ball Speed Over Over InsertMaterial Head MOI Robustness San Diego MHStar Face insert 400 Ti 6-4BL-1 5200 0.053 69%  51% Face insert 400 6061 Aluminum BL-1 5200 0.06464%  41% Face insert 400 304 SS BL-1 5200 0.085 51%  22% Microhinge StarDSM 550 BL-1 5200 0.108 38% N/A None 304 SS San Diego 4437 0.175 N/A−61%

The method of the present invention optimizes golf balls and clubs foruse with each other, while keeping these products in conformance withtheir respective rules. Simultaneous design gives a larger design spacefor exploration.

FIG. 6 is an iron-type face insert with a variable thickness patternderived from the method shown in FIG. 1 .

From the foregoing it is believed that those skilled in the pertinentart will recognize the meritorious advancement of this invention andwill readily understand that while the present invention has beendescribed in association with a preferred embodiment thereof, and otherembodiments illustrated in the accompanying drawings, numerous changes,modifications and substitutions of equivalents may be made thereinwithout departing from the spirit and scope of this invention which isintended to be unlimited by the foregoing except as may appear in thefollowing appended claims. Therefore, the embodiments of the inventionin which an exclusive property or privilege is claimed are defined inthe following appended claims.

I claim as my invention the following:
 1. A non-transitory computerreadable medium storing instructions that optimize a structure of aputter head for ball speed robustness, when executed by a processor,cause the processor to: generate a plurality of face thickness pointsand a plurality of body thickness points using a sampling technique tofill a design space using a finite element analysis (“FEA”) program togenerate a plurality of responses comprising a plurality of performancecharacteristics for the putter head; generate a surrogate model from theplurality of responses comprising generating a function for durabilityof the putter head from a finite element analysis (“FEA”) program of theputter head using the plurality of face thickness points for the golfclub head and the plurality of body thickness points for the putterhead, generating a function for ball speed robustness of the putter headfrom the FEA program using the plurality of face thickness points forthe putter head and the plurality of body thickness points for theputter head; use the surrogate model in an optimization algorithm toprovide an approximation of a lower sample space; and repeat theabove-mentioned steps until the surrogate model converges with the FEAfor a predetermined objective to optimize the structure of the putterhead for ball speed robustness.
 2. The non-transitory computer readablemedium according to claim 1 wherein use the surrogate model in anoptimization algorithm to provide an approximation of a lower samplespace comprises inputting a constrained function for durability and thefunction for ball speed robustness into a meta-modeled basedoptimization algorithm to generate an optimized structure for the putterhead for ball speed robustness.
 3. A non-transitory computer readablemedium storing instructions that optimize a structure of an iron-typeclub head for ball speed, when executed by a processor, cause theprocessor to: generate a plurality of face thickness points and aplurality of body thickness points using a sampling technique to fill adesign space using a finite element analysis (“FEA”) program to generatea plurality of responses comprising a plurality of performancecharacteristics for the iron-type club head; generate a surrogate modelfrom the plurality of responses comprising generating a function fordurability of the iron-type club head from a finite element analysis(“FEA”) program of the iron-type club head using the plurality of facethickness points for the iron-type club head and the plurality of bodythickness points for the iron-type club head, generating a function forball speed of the iron-type club head from the FEA program using theplurality of face thickness points for the iron-type club head and theplurality of body thickness points for the iron-type club head; use thesurrogate model in an optimization algorithm to provide an approximationof a lower sample space; and repeat the above-mentioned steps until thesurrogate model converges with the FEA for a predetermined objective tooptimize the structure of the iron-type club head for ball speed.
 4. Thenon-transitory computer readable medium according to claim 3 wherein usethe surrogate model in an optimization algorithm to provide anapproximation of a lower sample space comprises inputting a constrainedfunction for durability and the function for ball speed into ameta-modeled based optimization algorithm to generate an optimizedstructure for the iron-type club head for ball speed.